The present invention described herein relates to the field of optical monitoring of a rough surface. More specifically, the invention relates to optically monitoring the longitudinal position of a rough surface to interferometric precision.
Monitoring of rough surfaces to interferometric precision may be accomplished by known techniques employing holographic interferometry, and speckle photography. See R. K. Erf, editor, "Speckle Metrology", Academic Press, New York, 1978. These techniques produce a plurality of interference fringes across an image surface, and they require photographic film development or use of a TV camera and electronic subtraction to provide good fringe contrast. See J. N. Butters, R. Jones, and C. Wykes, "Electronic Speckle Pattern Interferometry", in "Speckle Metrology", by R. K. Erf, editor described above. It would be desirable, however, to be able to monitor a surface with interferometric precision without using film and the requisite steps for film development, or computer processing.
Other known techniques include the use of phase conjugating media instead of photographic film to implement holographic interferometry. See J. P. Huignard and J. P. Herriau, "Real-time double-exposure interferometry with Bi.sub.12 SiO.sub.20 crystals in transverse electrooptic configuration", Appl. Opt., 1807-1809, 1977 and T. Sato, T. Hatsuzawa, and O. Ikeda, "Dynamic interferometric observation of differential movement", Appl. Opt., 3895-3897, 1983. Characteristically, with phase conjugating media, a plurality of interference contours cross the image of the surface being measured.
In Huignard et al. and Sato et al. mentioned above, an optical wavefront is transmitted through a transparent object and is recorded holographically in an initial exposure. Then, subsequent wavefront information is obtained from the object at a later time in the manner of double exposure holographic interferometry. The initial wavefront information is compared with the wavefront information obtained subsequently, and the comparison provides information about changes in the object over time. Phase conjugation is not used in these techniques of Huignard et al. and Sato et al. although the Bi.sub.12 SiO.sub.20 (BSO) crystal used to record the exposures has also been used in phase conjugation. Although not actually disclosed in the articles of Huignard et al. and Sato et al, their techniques could, in principle, be used to examine opaque surfaces in reflection. But even so, a plurality of fringes would extend across the field, and the spacing and positioning of the plurality of fringes would change as the object position and orientation would change. It would be desirable, however, to be able to make surface measurements with interferometric precision without employing double exposures separated in time.
The prior art also discloses U.S. Pat. No. 4,280,764 by L. Sica and H. Szu for a "Phase-Conjugate Interferometer." In this patent, it is disclosed that the phase conjugate to a given wavefront could serve as a reference for that wavefront in an interferometric measurement of its phase. The basic apparatus arrangement includes a Michelson interferometer with one of the mirrors replaced by a phase-conjugating mirror. The phase conjugator acting on an optical signal, represented by Aexp(i.theta.), produces the complex conjugate of the spatial portion of the signal, represented by Aexp(-i.theta.), where A is the nonnegative real amplitude of the light wave, and .theta. specifies its phase. In particular, .theta.=[2.pi.f(x,y).lambda.], where .lambda.is the signal's wavelength, and f(x,y) specifies the optical path variations perpendicular to the direction of the signal propagation, the z direction. Thus .theta. is a distance in the z direction expressed in radians. The sum of the two wavefronts as produced with an interferometer is 2Acos.theta., and the corresponding observed intensity at the output is 4A.sup.2 cos.sup.2 .theta.. Thus, by a computation, the measurement of intensity allows the calculation of the phase of the input light wave. This technique provides an image of an interference pattern. It would be desirable, however, to conduct measurements with interferometric precision that do not require the use of an interference pattern image.
In additional prior art, I. Bar-Joseph, A. Hardy, Y. Katzir, and Y. Silberberg, "Low-power phase-conjugate interferometry", Opt. Lett., vol. 6, page 414, 1981, the phase-conjugate wave is produced with a phase conjugator, using two pump beams. In J. Feinberg, "Interferometer with a self-pumped phase-conjugating mirror," Opt. Lett., vol. 8, 569-571, 1983, the phase-conjugate wave is produced in the photorefractive crystal BaTiO.sub.3 which allows the process of self-pumping, i.e. where no external reference beams are required for the phase-conjugation process.
Both externally pumped (externally referenced) and self-pumped (self-referenced) phase-conjugate waves provide the desired light wave interference for interferometry. However, there is a difference between them. In the process of self-pumping described in the above-mentioned article by Feinberg, sensitivity to spatially uniform phase shifts of the input wave to the phase conjugator is lost. (By uniform, it is meant entirely longitudinal, i.e. along the z direction. This kind of phase shift is not conjugated by a self pumped phase conjugate mirror. Contrast this with a transverse phase variation, i.e. one which occurs at least in part in a spatial direction transverse to z. Such a phase shift in general affects the form and spacing of interference fringes in an interferometer. Reflection from a rough surface produces such disturbances. This means that a spatially constant phase shift due to, for example, placing a glass plate in the self phase conjugator arm of the interferometer is not compensated, resulting in a shift in the output fringe system just as in the case for a normal non-phase-conjugating mirror. The occurrence of this phase shift at the interferometer output does not take place for a phase conjugator that uses external reference beams as is also demonstrated in the same Feinberg article. In case of external reference beams, a longitudinal phase shift introduced into the conjugating arm of the interferometer is compensated, and there is no shift of the output fringes. It would be desirable, therefore, to provide a technique for measuring surfaces with interferometric precision which combines properties of both self-referenced and externally referenced phase conjugators. It is desirable to do this when surface location or displacement is important irrespective of lack of optical flatness.
In other prior art, P. Yeh, M. D. Ewbank, M. Khoshnevisan, and J. M. Tracy in "Doppler-free phase-conjugate reflection", Opt. Lett., vol. 9, 41-43, 1984 disclose that the reflection from a moving phase-conjugate mirror does not exhibit a Doppler shift in frequency using four-wave mixing, including externally pumped reference waves, with photorefractive Bi.sub.12 SiO.sub.20 (BSO) in a phase-conjugate Michelson interferometer. This reference discloses a beam splitter and two mirrors, one of which is a conventional mirror and the other of which is a phase-conjugate mirror. Both the mirrors are stationary in a frame of reference. Reflected beams from both the stationary mirror and the phase-conjugate mirror recombine and interfere at a detector, and an angular beat frequency of 2.delta. is observed due to motion of an external mirror. A piezoelectric transducer is used to modulate the position of the plane mirror and thereby the frequency of light reflected from it, which light is input into the phase conjugate mirror. As a result, the interferometer exhibited variation in the output intensity as a function of the piezoelectric transducer motion. It would be desirable, however, to provide a technique for measuring the positional changes of rough surfaces, as well as the optically finished surfaces used in the above reference, with interferometric precision.